Kepler’s laws agree with all observed planetary motions, and by the table in the previous section, they give the correct proportions of all planetary orbits. If the mean distance of Earth from the Sun is 1 AU (“Astronomical Unit”), then that of Venus is 0.723 AU, of Mercury 0.387 AU and that of Mars is…
Fig. 1 The 2004 Venus transit observed from 3 locations by the GONG collaboration Kepler’s third law allows one to evaluate the dimensions of the solar system in relative units, e.g. in “astronomical units” (AUs), where 1 AU is the mean Sun-Earth distance. However, to express the AU in kilometers or in miles seems to require some sort of parallax–some difference…
We’ve been paying a lot of attention to Venus and its orbital patterns, as did scientist Edmund Halley hundreds of years ago. Back then he came up with a plan to determine Earth’s distance to the sun, the AU. Two key components were Kepler’s Astronomical Unit, or AU, and an angle, α, which formed between lines of…
As Already Discussed Newton’s equation to calculate the sun’s gravitational force acting upon Earth, and here we’ll begin solving for the last remaining unsolved variable within that equation, v, Earth’s orbital velocity. Here again is Newton’s equation, Fg = [m × v2] ÷ r For a refresher on how we solved for m, Earth’s mass, and r, the distance between…
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. Due to foreshortening, nearby objects show a larger parallax than farther objects when observed from different positions, so parallax can be used to determine distances. To measure…
Last topic we learned that the bigger an optical rangefinder, the better its accuracy in measuring distant objects. here we’ll take that concept a step further when we discover how Earth itself was used by ancient scientists to gauge its distance to the moon. Here will be strewn with embedded links to previous topics in this series, all…
Last time we discussed the fact that ultra fine gradations must be applied to a rangefinder’s indicator gauge in order to make accurate measurements of extremely long distances. Today we’ll see how using a bigger rangefinder effectively solves this problem. Figure 1 illustrates the subject. The left side shows what happens when attempting to use a small rangefinder to measure the…
As We discussed earlier that when optical rangefinders are used to measure the distance to objects extremely far away we encounter problems. We discussed one of them last time, the fact that as θ approaches 90° the tangent of θ becomes asymptotic, resulting in a situation where even the most minute changes to θ bring about…
We’ve been looking at the indirect methods employed by scientists through the ages as they struggled to determine the distance of our Earth from its sun. Today we’ll take a look at one of those indirect methods, known in scientific circles as the Principle of Parallax. Parallax is an optical effect which results in a three dimensional…
Last time we discussed the term acceleration of gravity, a physical phenomenon posited by Sir Isaac Newton in his book Philosophia Naturalis Principia Mathematica. Newton’s Law of Gravitation is also presented in this book. It provides the basis for his mathematical formula to calculate the acceleration of gravity, g, for any heavenly body in the universe. Newton’s formula to…